Empirical Analysis Of Stock Index Return Rate Based On ARMA-Copula-DCC-Garch Models

This thesis studies the yields of the three most influential indices of the Shanghai Composite Index,the Hang Seng Index and the Nikkei 225 Index,as well as the modeling of volatility and correlation.The ARMA model is used to extract the information of the yield level,and then the multivariate GARCH model is built for the residual.The structure of dependencies between assets may change over time,requiring a dynamic condition correlation model(DCC).The structure that depends on the residuals may not be multivariate normal,and it is necessary to introduce a Copula connection function to connect various edge distributions.In terms of evidence,this thesis analyzes the yields of the Shanghai Composite Index,Hang Seng Index and Nikkei 225 Index in Asia.Firstly,the ARMA-GARCH model is established independently,and the obtained ARMA order(2,3)is used as the order of the edge distribution level information extracted from the multivariate GARCH.The t-copula connection residual is selected because the financial yield has the characteristics of thick tail and spike.Then the parameters of the t-Copula-DCC-GARCH model are obtained by the method of maximum likelihood function.The results show that the Shanghai Stock Index and the Constant Birthday Index The dynamic correlation coefficient has grown tremendously from 1999 to the present,with 4 to 5 structural changes.